When to eat your brown dwarf: At breakfast, lunch or dinner?

Tristan GuillotObservatoire de la Côte d’Azur

Doug Lin (UCSC), Pierre Morel (OCA)

A&A stuff

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M-Teff relation

3000 4000 5000 6000 7000Teff [K]

0.01

0.10

1.00

10.00

100.00

M s

ini [

MJu

p]

P [days]

1

10

100

[Fe/H]

-0.5

0.0

0.5

Bouchy et al. (2011)

3000 4000 5000 6000 7000Teff [K]

0.01

0.10

1.00

10.00

100.00

M s

ini [

MJu

p]

P [days]

1

10

100

[Fe/H]

-0.5

0.0

0.5

M-Teff relation

3000 4000 5000 6000 7000Teff [K]

0.01

0.10

1.00

10.00

100.00

M s

ini [

MJu

p]

CoRoT-11 b

CoRoT-15 b

CoRoT-2 b

CoRoT-3 b

OGLE-TR-122 b

WASP-30 b

CoRoT-14 b

WASP-19 b

WASP-18 bHAT-P-20 b CoRoT-14 b

CoRoT-15 b

CoRoT-27 b

CoRoT-3 b

HAT-P-20 b

HAT-TR-205-013 b

HD 41004 B b

KELT-1 bNLTT 41135C b

OGLE-TR-106 bOGLE-TR-123 b

TYC 2930-00872 b

WASP-14 bWASP-18 b

WASP-30 b

WASP-89 b

XO-3 b

tau Boo b

P [days]

1

10

100

[Fe/H]

-0.5

0.0

0.5

M-Teff relation

3000 4000 5000 6000 7000Teff [K]

0.01

0.10

1.00

10.00

100.00

M s

ini [

MJu

p]

P [days]

1

10

100

[Fe/H]

-0.5

0.0

0.5

M-Teff relation

Conjecture: Massive planets and brown

dwarfs in this region have been swallowed by their star due to tidal interactions

Probabilities

0.01 0.10 1.00 10.00 100.00M2 [MJup]

0.0

0.2

0.4

0.6

0.8

1.0

P(T

eff>

6000K

& M

2>

M2,i)

Porb<5 days

Porb>5 days

3000 4000 5000 6000 7000Teff [K]

0.01

0.10

1.00

10.00

100.00

M s

ini [

MJu

p]

P [days]

1

10

100

[Fe/H]

-0.5

0.0

0.5

3000 4000 5000 6000 7000Teff [K]

0.01

0.10

1.00

10.00

100.00

M s

ini [

MJu

p]

P [days]

1

10

100

[Fe/H]

-0.5

0.0

0.5

Porb<5days Porb>5days

Consequences of tidal interactions

• Circularization

• Orbital migration

• Critically depends on period and Q parameter• Q measures the efficiency of

dissipation

• Q is determined to be around 105 to 106 for the circularization of binary stars

4000 5000 6000 7000Teff [K]

104

106

108

1010

1012

t mig

ratio

n [y

ears

]

tau Boo

CoRoT-15CoRoT-18 CoRoT-2

CoRoT-3

OGLE-TR-122

WASP-30

CoRoT-14WASP-19

WASP-18 OGLE-TR-123

WASP-33

HAT-TR-205-013WASP-12

M [Mjup]

1

10

100

Q'*=106

Q’*=106: migration timescales

ModelSolves the tidal evolution of star+companion in the planar case(assumes Q α n)

Stellar evolution models (CESAM2k) are included (radius, moment of inertia, convective zones)

Magnetic breaking is taken into account

The companion’s radius is fixed = 1Rjup

Initial conditions are based on the observed, present-day population

Guillot, Lin & Morel, in preparation Dynamical equations: Barker & Ogilvie (2009)

The sources of dissipation in the star

• Constant Q model• Requires Q*>108

• Cannot explain the tmig-Teff correlation

• Dissipation of internal gravity waves(Goodman & Dickson 1998, Barker & Ogilvie 2010, 2011)

• Only in stars with a radiative center

• Only for companions with masses above a critical mass (>3 Mjup for a 5Ga Sun)

• Dissipation of inertial waves (Ogilvie & Lin 2004, 2007)

• Limited to a narrow frequency range

The IGWs prescription

The gravity waves break and dissipate near the stellar center if there is a radiative core and if the perturbing amplitude is large enough, i.e., for the present Sun:

In that case the tidal dissipation factor is:

Otherwise, we assume

Q’=107 to 1010

Barker & Ogilvie (2010)

0.00 0.01 0.02 0.03Radius [RSun]

-0.0005

0.0000

0.0005

0.0010

0.0015

0.0020

Wav

e di

spla

cem

ent [

RS

un]

1 Mjup

3 Mjup

10 Mjup

30 Mjup

Non-linear

The critical mass for dissipation

0.00 0.01 0.02 0.03Radius [RSun]

-0.0005

0.0000

0.0005

0.0010

0.0015

0.0020

Wav

e di

spla

cem

ent [

RS

un]

1 Mjup

3 Mjup

10 Mjup

30 Mjup

Non-linear

Stellar evolution models

Magnetic braking

We assume a=1, n=1.5 and find Kw=1.5x10-14 yr-1, in agreement with Bouvier et al. 1997

We add a factor Min(1,mcz/m0) where mcz is the mass of the outer convective zone/total mass and m0=6x10-4 to account for the fact that massive stars have a slower braking

4000 5000 6000 7000 8000Teff [K]

-1

0

1

2

3

Log(v

sini) [km

/s] mcz

*=0

mcz*=10-2

mcz*=10-3

SPOCS + Nordstrom

Constant dissipation model: Q’*=108

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

life

time

/ma

in s

eq

ue

nce

ag

e

0.8 0.9 1.0 1.1 1.2 1.3 1.4Mstar [MSun]

-1

0

1

2

log

(Mp)

[MJu

p]

CoRoT-14 b

CoRoT-15 b

CoRoT-27 b

CoRoT-3 b

HAT-P-20 b

HAT-TR-205-013 b

KELT-1 b

OGLE-TR-106 b OGLE-TR-123 b

TYC 2930-00872 b

WASP-14 b WASP-18 b

WASP-30 b

WASP-89 b tau Boo b

Q’*=108

Pini=3days

Constant dissipation model: Q’*=106

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

life

time

/ma

in s

eq

ue

nce

ag

e

0.8 0.9 1.0 1.1 1.2 1.3 1.4Mstar [MSun]

-1

0

1

2

log

(Mp)

[MJu

p]

CoRoT-14 b

CoRoT-15 b

CoRoT-27 b

CoRoT-3 b

HAT-P-20 b

HAT-TR-205-013 b

KELT-1 b

OGLE-TR-106 b OGLE-TR-123 b

TYC 2930-00872 b

WASP-14 b WASP-18 b

WASP-30 b

WASP-89 b tau Boo b

Q’*=106

Pini=3days

Internal gravity wave: full model

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

life

time

/ma

in s

eq

ue

nce

ag

e

0.8 0.9 1.0 1.1 1.2 1.3 1.4Mstar [MSun]

-1

0

1

2

log

(Mp)

[MJu

p]

CoRoT-14 b

CoRoT-15 b

CoRoT-27 b

CoRoT-3 b

HAT-P-20 b

HAT-TR-205-013 b

KELT-1 b

OGLE-TR-106 b OGLE-TR-123 b

TYC 2930-00872 b

WASP-14 b WASP-18 b

WASP-30 b

WASP-89 b tau Boo b

IGW

Pini=3days

Internal gravity wave: full model

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

life

time

/ma

in s

eq

ue

nce

ag

e

0.8 0.9 1.0 1.1 1.2 1.3 1.4Mstar [MSun]

-1

0

1

2

log

(Mp)

[MJu

p]

CoRoT-14 b

CoRoT-15 b

CoRoT-27 b

CoRoT-3 b

HAT-P-20 b

HAT-TR-205-013 b

KELT-1 b

OGLE-TR-106 b OGLE-TR-123 b

TYC 2930-00872 b

WASP-14 b WASP-18 b

WASP-30 b

WASP-89 b tau Boo b

IGW

Close-in, massive companions are lost

Too much orbital angular momentum

F stars loose angular momentum more slowly and tidal

dissipation by IGWs is not possible

Low mass companions are below critical limit for IGWs dissipation except at old ages

Pini=3days

3000 4000 5000 6000 7000Teff [K]

0.01

0.10

1.00

10.00

100.00

M s

ini [

MJu

p]

CoRoT-11 b

CoRoT-15 b

CoRoT-2 b

CoRoT-3 b

OGLE-TR-122 b

WASP-30 b

CoRoT-14 b

WASP-19 b

WASP-18 bHAT-P-20 b CoRoT-14 b

CoRoT-15 b

CoRoT-27 b

CoRoT-3 b

HAT-P-20 b

HAT-TR-205-013 b

HD 41004 B b

KELT-1 bNLTT 41135C b

OGLE-TR-106 bOGLE-TR-123 b

TYC 2930-00872 b

WASP-14 bWASP-18 b

WASP-30 b

WASP-89 b

XO-3 b

tau Boo b

P [days]

1

10

100

[Fe/H]

-0.5

0.0

0.5

Is it breakfast or dinner-time for CoRoT-2?

CoRoT-2

• CoRoT-2 is a wide binary (Poppenhaeger & Wolk 2014)• CoRoT-2A is a G7V with a 3.5 Mjup companion

• Apparent age: 0.1-0.3 Ga

• CoRoT-2B is a K9V with a low X ray activity

• Apparent age: >5 Ga

• An old age helps putting back CoRoT-2Ab with the other inflated hot Jupiters

0.001 10.0001.0

1.8

0.010 0.100 1.000Age [Ga]

1.2

1.4

1.6

Rad

ius

[RJu

p]

0.8

0.9

1.0

1.1

1.2

Rad

ius

[100

,000

km

]

2x1029 erg s-1

10 29 erg s -1

3x1028 erg s-1

opacities x 30opacities x 30

1% K.E. (4.6x1027 erg s-1)

standard model

3x1029 erg s-1

Guillot & Havel (2011)

Dynamical evolution of CoRoT-2

2000 4000 6000 8000Age [Ma]

0

5

10

15

20

25

Period [days

]

Orbital periodStellar spin periodPlanet spin periodlog(Q*)

2000 4000 6000 8000Age [Ma]

0

2

4

6

8

10

12

Period [days

]Orbital periodStellar spin periodPlanet spin periodlog(Q*)

CoRoT-2 fiducial3.5Mjup, Pini=5days, e=0

CoRoT-2 massive35Mjup, Pini=5days, e=0

Does not agree with the lack of massive planets on close orbits around G dwarfs: - Q’* dependence upon Pspin implies weaker dissipation in massive planet case- When star & planet are locked, migration is governed by magnetic braking

timescale (see Damiani & Lanza 2015)

Planets for breakfast?

• Mazeh et al. (2015) show that “cool” KOIs are more aligned than “hot” KOIs (Teff>6250K)• up to Porb=50 days!

• Matsakos & Königl (2015) propose that this may be due to an early ingestion of planets• Swallowed planets would affect the angular momentum of

cool stars more than hot stars which have a faster rotation

• This assumes that the stellar rotation axis and the disk with planets are tilted initially

Conclusions

• There are very few brown dwarfs & massive planets as close companions to G dwarfs whereas they are present around F dwarfs

• This would be naturally explained by their engulfment

• Would explain the «close-in brown dwarf desert»

• Source of dissipation are still to be fully accounted for

• Low magnetic braking in F-dwarfs is a critical factor

• Internal gravity waves have the interesting properties but are unable to account for all observations

• Inertial waves can potentially help

• Role of eccentricity?

• We still don’t know when brown dwarfs get eaten…